Maths Portfolio Infinite Surds

In this mathematics portfolio we are instructed to investigate different expression of infinite surds in square root form and then find the exact value and statement for these surds.

INFINITE SURDS

The following expression is an example of an infinite surd.

The first ten terms of the surd can be expressed in the sequence:

From the tem terms of the sequence we can observe that the formula for the sequence is displayed as:

The results had to be plotted in a graph as shown below:

The graph above shows us the relationship between n and. We can observe that as n increases, also increases but each time less than before, suggesting that at a large certain point of n it stops increasing and just follows in a straight line.

From the tem terms of the sequence we can observe that the formula for the sequence is displayed as:

The results had to be plotted in a graph as shown below:

The graph above also shows us the relationship between n and. We can observe that as n increases, also increases but each time less than before, suggesting that at a large certain point of n it stops increasing and just follows in a straight line.

To find the exact infinite value for this sequence we would use the equation and rearrange in the correct way to find the value.

Finding the exact value for the surd

The exact value for the surd is 2 as the second answer does not fit in the problem

The results show us that the limitations found in the general statement are those that didn’t give an integer as a final answer. Therefore k has to be an integer, however not a decimal or a fraction as results wouldn’t be a whole number. It also isn’t possible to obtain an integer if k is a negative number because there is no square root for a negative number. For a pleasing result, 1+4k , needs to give a number that possesses a perfect square root, an integer.

I arrived at this general statement by subtracting the n term from the k, and like that finding out that the product of this subtraction is the n term to the power of 2. Like that I found the equation. By rearranging the formula to make k the subject I came to the conclusion that , the general statement.

The origin and a radius of r units drawn to some point in the four quadrant of the circle forming a right triangle with its sides x,y, and r and its acute angles ? and (90- ?) With a triangle in the graph above labeled with x,y and r as its sides, the value of cos?

The following changes are made in the original recursive relation:- 1. The starting population is taken to be 59999 2. In the relation un+1 = (-1 x 10-5) un2 + 1.6un , we subtract 2500 as this is the number which is removed every year.

right to .2 and .7, and then to 2 and 7, and lastly and increase of 20. 2. That there is an exponent or a power that must determine the functions rate of growth or decay. From the clear decrease in +Gx the exponent is likely to be negative, and

The scatter plot clearly shows an elongated ?s-curve,? where its goes from increasing with an increasing rate of change to increasing with a decrease in rate of change. From 1896 to 1932, there was a slow increase. From 1948-1988 the rate of change was greater than before.

while L2 represents the value of numerator (N) Image 2 Caption: Image 2 shows the range set which is -2? n ? 6 for the x-axis while -2 ? y ? 20 for the y-axis Image 3 Caption: Image 3 shows the general equation obtained by using Quadratic Regression.

The value of an approaches approximately 1.618 (i.e. an?1.618) but never reach it. In other words, as n gets larger, the difference with the successive term (also shown in the figures in the ?an+1 - an? column of the table)